The standard deviation of each column in a matrix can be determined using the following steps:
- Calculate the mean of each column in the matrix.
- For each element in a column, subtract the mean of that column from the element to get the deviation.
- Square each deviation.
- Calculate the average of the squared deviations for each column by dividing the sum of the squared deviations by the total number of elements in that column minus 1.
- Take the square root of the result obtained in step 4 to get the standard deviation of each column.
Mathematically, the formula to calculate the standard deviation of each column in a matrix can be represented as follows:
𝜎 = √(∑(xᵢ - 𝑥̄)²/(n-1))
Where:
- 𝜎: Standard deviation of a column
- xᵢ: Each element of the column
- 𝑥̄: Mean of the column
- n: Total number of elements in the column
Note that the process and formula are the same whether the matrix is a population or a sample. The only difference is the value of n used in the formula (n for a population and n-1 for a sample).